11

Lloyd

Princeton, 1950

All mathematicians live in two different worlds. They live in a crystalline world of perfect platonic forms. An ice palace. But they also live in the common world where things are transient, ambiguous, subject to vicissitudes. Mathematicians go backward and forward from one world to another. They’re adults in the crystalline world, infants in the real one. — S. CAPPELL, Courant Institute of Mathematics, 1996

AT TWENTY-ONE, Nash the mathematical genius had emerged and connected with the larger community of mathematicians around him, but Nash the man remained largely hidden behind a wall of detached eccentricity. He was quite popular with his professors, but utterly out of touch with his peers. His interactions with most of the men his own age seemed motivated by an aggressive competitiveness and the most cold considerations of self-interest. His fellow students believed that Nash had felt nothing remotely resembling love, friendship, or real sympathy, but as far as they were able to judge, Nash was perfectly at home in this arid state of emotional isolation.

This was not the case, however. Nash, like all human beings, wanted to be close to someone, and at the beginning of his second year at Princeton he had finally found what he was looking for. The friendship with Lloyd Shapley, an older student, was the first of a series of emotional attachments Nash formed to other men, mostly brilliant mathematical rivals, usually younger. These relationships, which usually began with mutual admiration and intense intellectual exchange, soon became one-sided and typically ended in rejection. The relationship with Shapley foundered within a year, although Nash never completely lost touch with him over the decades to follow — all through his long illness and after he began to recover — when he and Shapley became direct competitors for the Nobel Prize.

•   •   •

When he first moved into the Graduate College a few doors down from Nash in the fall of 1949, Lloyd Shapley had just turned twenty-six, five years and eleven days older than Nash.1 No one could have presented a stronger contrast with the childish, boorish, handsome, and uninhibited boy wonder from West Virginia.

Born and bred in Cambridge, Massachusetts, Shapley was one of five children of one of the most famous and revered scientists in America, the Harvard astronomer Harlow Shapley. The senior Shapley was a public figure known to every educated household, and also one of the most politically active.² In 1950, he was accorded the dubious honor of being the first prominent scientist to appear on the earliest of Senator Joseph McCarthy’s famous lists of crypto-communists.³

Lloyd Shapley was a war hero.⁴ He was drafted in 1943. He refused an offer to become an officer. That same year, as a sergeant in the Army Air Corps in Sheng-Du, China, Shapley got a Bronze Star for breaking the Japanese weather code. In 1945, he went back to Harvard, where he had begun to study mathematics before he was drafted, and finished his B.A. in mathematics in 1948.

When Shapley showed up at Princeton, von Neumann already considered him the brightest young star in game theory research.⁵ Shapley had spent the year after graduating from Harvard at the RAND Corporation, a think tank in Santa Monica that was attempting to use game theory applications to solve military problems, and came to Princeton while technically on leave from RAND. He was immediately recognized as brilliant and quite sophisticated in his thinking. One contemporary remembers that he “talked good math, knew a lot.”⁶ He did extraordinarily hard double crostics from The New York Times without using a pencil.⁷ He was a fiercely competitive and highly accomplished player of Kriegspiel⁸ and go. “Everybody knew that his game was strictly his own,” said another fellow student. “He went out of his way to find nonstandard moves. No one was going to anticipate them.”⁹ He was also well read. He played the piano beautifully.¹⁰ His manner suggested an acute awareness of pedigree and prospects. When Lefschetz wrote him a letter telling him of a very generous grant if he came to Princeton, for example, Shapley replied loftily and with a hint of disdain, “Dear Lefschetz, The arrangements are satisfactory. Go ahead with the formalities. Shapley.”¹¹

Shapley was by no means as self-confident as his imperious note to Lefschetz implied. His appearance can only be described as rather strange. Tall, dark, and so thin that his clothing hung from him like a scarecrow’s, Shapley reminded one young woman of a giant insect; another contemporary says he looked like a horse.¹² His normally gentle demeanor and ironic banter hid a violent temper and a harshly self-critical streak.¹³ When challenged in some unexpected fashion, he could become hysterical, literally vibrating and shaking with fury.¹⁴ His perfectionism, which would later prevent him from publishing a large portion of his research, was extreme.¹⁵ He was, moreover, acutely self-conscious about being a few years older than some of the brilliant young men around the Princeton mathematics department.¹⁶

Nash was one of the first students Shapley met at the Graduate College. For a time, they shared a bathroom. Both of them attended Tucker’s game theory seminar every Thursday, now run by Kuhn and Gale while Tucker was at Stanford. The best way to describe the impression Nash made on Shapley when the two first talked about mathematics is to say that Nash took Shapley’s breath away. Shapley could, of course, see what the others saw — the childishness, brattiness, obnoxiousness — but he saw a great deal more. He was dazzled by what he would later describe as Nash’s “keen, beautiful, logical mind.”17 Instead of being alienated like the others by the younger man’s odd manner and weird behavior, he interpreted these simply as signs of immaturity. “Nash was spiteful, a child with a social IQ of 12, but Lloyd did appreciate talent,” recalled Martin Shubik.¹⁸

•   •   •

As for Nash, starved for affection, how could he not be drawn to Shapley? In Nash’s eyes, Shapley had it all. A brilliant mathematician. War hero. Harvard man. A son of Harlow. Favorite of von Neumann and, soon, of Tucker as well. Shapley, who was popular with faculty and students alike, was one of the very few around Princeton, other than Milnor, who could really hold Nash’s attention in a mathematical conversation, challenge him, and help him to pursue the implications of his own reasoning. And, for that reason — along with his open admiration and obvious sympathy — he was one who could engage Nash’s emotions.

Nash acted like a thirteen-year-old having his first crush. He pestered Shapley mercilessly.¹⁹ He made a point of disrupting his beloved Kriegspiel games, sometimes by sweeping the pieces to the ground. He rifled through his mail. He read the papers on his desk. He left notes for Shapley: “Nash was here!” He played all kinds of pranks on him.

Shapley’s greatest eccentricity at the time was his claim that he was on a twenty-five-hour sleep cycle.²⁰ He worked and slept at extremely odd hours, often transposing night and day. “Every once in a while he’d disappear from sight,” another student recalled. “That’s what he said. We accepted anything.”²¹ Waking Shapley when he was lost to the world became an ongoing prank. “A group of us was attending a regular seminar at the institute given by de Rham and Kodaira. We were always very anxious to go but only three or four of us had cars. Lloyd Shapley was one but there was one difficulty. Lloyd liked to sleep late and was often asleep at two o’clock in the afternoon. So we had to devise all sorts of ways to wake him. We dropped hot candle wax on him. I devised another method. We played 45-rpm records of Lloyd’s favorite Chinese music without the little insert so that it oscillated all over the place (and made excruciating noise).”²² Nash once tried to wake Shapley by climbing on his bed, straddling him and dropping water in his ear with an eyedropper.²³

Sometimes the jokes, also aimed at other friends of Shapley’s, got totally out of hand. Shapley shared his room at the college with a graduate student in economics, Martin Shubik, who became interested in game theory and also developed a lifelong friendship with Shapley. Shubik recalled: “Nash’s idea of a joke was to unscrew the electric light bulb in the bathroom. There was a glass shade under the bulb, which he filled full of water. We could easily have gotten electrocuted. Did he intend to electrocute me? I’m not sure he didn’t intend to.”²⁴

Shubik, whom Nash insisted on calling Shoobie-Woobie, was a frequent target of Nash’s digs. A typical putdown, from a postscript to a note ostensibly commiserating with Shubik after the latter was injured in a car accident: “Oscar le Morgue would like for someone . . . to blast Baumol [William Baumol, then the rising young star of the Princeton economics department] for his impudence in publishing a paper attacking confusedly the only true utility. It’s beneath his dignity, but he doesn’t really think you’re the best man for the job because . . . ‘Shubik does not write very clearly.’ “25

John McCarthy, one of the inventors of artificial intelligence, also befriended Shapley and apparently aroused Nash’s jealousy. One day McCarthy got an inquiry from a Philadelphia haberdashery about a massive shirt order he had placed.²⁶ How good was his credit, the company wanted to know? McCarthy, who hadn’t placed any such order, immediately suspected Nash and asked Shapley if Nash was the culprit. Shapley confirmed that this was highly likely. McCarthy asked the company for the original order. Sure enough, a postcard came back with Nash’s unmistakable scrawl in green ink, the color Nash always used. Shubik and McCarthy cornered Nash and confronted him. “There was no denying what he had done. We threatened him with postal inspectors. The post office refused to merely bawl him out. ‘If we do anything, we’ll prosecute him,’ they said.” Concluding that Nash had learned his lesson, Shubik and McCarthy dropped the matter. Another time, he rigged up McCarthy’s bed so that it would collapse when McCarthy tried to crawl under the covers.²⁷

It was Shapley who reacted to Nash’s absurd behavior with amused tolerance, who proposed that they might channel his mischievous impulses in a more intellectually constructive way. So Nash, Shapley, Shubik, and McCarthy, along with another student named Mel Hausner, invented a game involving coalitions and double-crosses. Nash called the game — which was later published under the name “So Long, Sucker” — Fuck Your Buddy.²⁸ The game is played with a pile of different-colored poker chips. Nash and the others crafted a complicated set of rules designed to force players to join forces with one another to advance, but ultimately to double-cross one another in order to win. The point of the game was to produce psychological mayhem, and, apparently it often did. McCarthy remembers losing his temper after Nash cold-bloodedly dumped him on the second-to-last round, and Nash was absolutely astonished that McCarthy could get so emotional. “But I didn’t need you anymore,” Nash kept saying, over and over.²⁹

By and large, Shapley tried to play the role of mentor. He came to Nash’s aid, for example, when Tucker demanded that Nash include a concrete example of an equilibrium point in his thesis and Nash couldn’t think of a good one. Shapley spent weeks working out an elaborate but convincing example of Nash’s equilibrium concept involving three-handed poker, another Shapley specialty.³⁰

•   •   •

The friendship between the men always had a competitive edge.³¹ Shapley, who started out as the slightly older and wiser half of the relationship, may have resented Nash’s reputation as a genius. He kept remarking on “running starts,” and he made it clear that he felt he was being left behind.32 Nash’s stubborn independence in the face of well-meant advice, instead of delighting, began to irk. Nash’s real sin, though, may have been to publish three important papers in the space of one year, long before Shapley had even come close to finding a thesis topic for himself.³³ In one of them, Nash beat Shapley to the punch on a problem they were both working on and had spent many hours discussing.³⁴

But Shapley actually had good reason to feel secure. Despite Nash’s brilliant dissertation, the consensus at Princeton at the time was that it was Shapley who was the real star of the next generation and inheritor of the von Neumann mantle. Tucker wrote in 1953: Shapley is “the best young American mathematician working in the subject.”³⁵ As a person, Tucker added, Shapley is “agreeable, cooperative and well-liked by faculty and students.”³⁶ A letter from Frederic Bohnenblust, Shapley’s mentor at RAND, dated 1953, says Shapley “perhaps lacked the wherewithal to develop a theory and depended on others for ideas,” but added that he thought him “second only to the creator of the theory of games, John von Neumann.”³⁷ A letter from von Neumann dated January 1954 said: “I know Shapley very well and I think he is VERY good. I would put him above Bohnenblust and I would bracket him with Segal and Birkhoff.”³⁸

But something other than graduate-student rivalry caused a sudden break. By the middle of the next year, by which time Nash had already completed his thesis and was on the job market, Shapley told a fellow student that he would not return to RAND if Nash, who had been offered a permanent post there, were to accept it.³⁹ Fifty years later, Shapley made a point of correcting anyone who suggested that he and Nash had ever been close friends.⁴⁰